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Solve 2x² + 4x + 2 = 0

The solution of 2x² + 4x + 2 = 0 is x = -1 (a repeated root).

x² +x += 0
2x2+4x+2=0⇒x=−12x^2 + 4x + 2 = 0 \Rightarrow x = -1
Discriminant D = 0 · x ≈ -1

Change a, b or c (whole numbers, a not 0) and the exact solutions follow.

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Graph of y = 2x² + 4x + 2-3.5-3-2.5-2-1.5-1-0.50.511.524681012x = -1vertexy = 2x² + 4x + 2
Graph of y = 2x² + 4x + 2. The curve crosses the x-axis at x = -1; the vertex is at (-1, 0).

How to work it out

  1. 1

    Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = 2, b = 4, c = 2.

    2x2+4x+2=02x^2 + 4x + 2 = 0
  2. 2

    Work out the discriminant D = b² − 4ac. Its sign tells you how many real solutions there are.

    D=42−4⋅2⋅2=16−16=0D = 4^2 - 4\cdot2\cdot2 = 16 - 16 = 0
  3. 3

    D is zero, so there is exactly one solution (a repeated root).

  4. 4

    Method 1, factoring. The roots are rational, so the left side factors:

    2(x+1)(x+1)=02\left(x + 1\right)\left(x + 1\right) = 0
  5. 5

    A product is zero when one of its factors is zero, so set each factor equal to 0 and solve:

    x+1=0⇒x=−1x + 1 = 0 \Rightarrow x = -1
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=−4±04x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-4 \pm \sqrt{0}}{4}
  7. 7

    Simplify to get the solution:

    x=−1x = -1
  8. 8

    Check by putting x = -1 back in: a·x² + b·x + c = 2·(1) + 4·(-1) + 2 = 0 ✓

LaTeX source of the formulas on this page
\[ 2x^2 + 4x + 2 = 0\ \Rightarrow\ x = -1 \]
\[ 2x^2 + 4x + 2 = 0 \]
\[ D = 4^2 - 4\cdot2\cdot2 = 16 - 16 = 0 \]
\[ 2\left(x + 1\right)\left(x + 1\right) = 0 \]
\[ x + 1 = 0 \Rightarrow x = -1 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-4 \pm \sqrt{0}}{4} \]
\[ x = -1 \]

The parabola y = 2x² + 4x + 2

xy
-418
-38
-22
-10
02
18
218

Questions

What are the solutions of 2x² + 4x + 2 = 0?

The solution of 2x² + 4x + 2 = 0 is x = -1 (a repeated root).

Does 2x² + 4x + 2 = 0 factor?

Yes: 2(x+1)(x+1) = 0.

What is the vertex of y = 2x² + 4x + 2?

(-1, 0). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = -2, product = c/a = 1.

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